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Some quick thoughts as specifically related to inflation expectations estimation
BEIs = expected inflation + inflation risk premium - TIPS liquidity effect + model error
Below I'm going to discuss how expected inflation is estimated which is really where all the debate is https://twitter.com/ernietedeschi/status/1359152721409040384
BEIs = expected inflation + inflation risk premium - TIPS liquidity effect + model error
Below I'm going to discuss how expected inflation is estimated which is really where all the debate is https://twitter.com/ernietedeschi/status/1359152721409040384
These pieces are jointly estimated by:
- using a latent factor structure
-a VAR which controls these factor's dynamics
-a no arb term-structure model that decomposes yields into expectations and risk premia
If you want the best overview read https://www.bankofengland.co.uk/-/media/boe/files/working-paper/2014/expectations-risk-premia-and-information-spanning-in-dynamic-term-structure-model-estimation.pdf
- using a latent factor structure
-a VAR which controls these factor's dynamics
-a no arb term-structure model that decomposes yields into expectations and risk premia
If you want the best overview read https://www.bankofengland.co.uk/-/media/boe/files/working-paper/2014/expectations-risk-premia-and-information-spanning-in-dynamic-term-structure-model-estimation.pdf
TIPS have only been around for ~20 years. As a result we only have two complete business cycles worth of data for them. This makes estimating any sort of time-series model quite challenging
To get around this, DKW and many other related papers, augment TIPS data with surveys
To get around this, DKW and many other related papers, augment TIPS data with surveys
The inclusion of surveys makes allows us to bring in outside data + expert judgement about the economy (its very hard to beat the SPF surveys over short horizons)
These surveys help ensure that the dynamics of the estimated VAR are reasonable and make the model much more stable
These surveys help ensure that the dynamics of the estimated VAR are reasonable and make the model much more stable
Historically the surveys have just assumed that current inflation would head up towards its target over the forecast relevant horizon (asymptotically without overshooting; think of it as AR(1) vs AR(2) dynamics). The model's very inertial
DKW also assumes the level of inflation is mean-reverting over-time
It doesnt necessarily look like this because the model is so inertial that long-run expectations closely track long-run surveys (a key trick that allows a simpler to estimate model some extra realism)
It doesnt necessarily look like this because the model is so inertial that long-run expectations closely track long-run surveys (a key trick that allows a simpler to estimate model some extra realism)
But this very slow mean reversion means that AIT-like strategies dont really align with the estimated dynamics for expected/observed inflation that the model's dynamics are capable of producing.
We have to think about expectations being a function of two things:
- the factors at any given point (based on surveys, TIPS, observed inflation)
- the estimated dynamics in the factor VAR
- the factors at any given point (based on surveys, TIPS, observed inflation)
- the estimated dynamics in the factor VAR
If the estimated VAR just believes the "true" dynamic of inflation over a long-horizon is asymptotic mean-reversion it will be almost impossible for expected inflation to exhibit overshooting
Also DKW's liquidity effect is behaving oddly just as it did during the other lowest period of real & nominal rates. To me this is good evidence that the model is implicitly mis-specified when real and nominal rates are so far from their mean
As a quick disclosure: my model from fall 2020 suffers from this same lack of overshooting. It allows for a time-varying trend in inflation but doesnt have overshooting. Its been more adaptive and doesnt have a + liquidity effect
https://twitter.com/peterdwilliams/status/1356634400579018754?s=20 https://twitter.com/peterdwilliams/status/1351641355668365319?s=20
https://twitter.com/peterdwilliams/status/1356634400579018754?s=20 https://twitter.com/peterdwilliams/status/1351641355668365319?s=20
How could we fix this issue: We need better expectations data!
Because AIT changes the nature of medium-term inflation forecasts, existing model dynamics wont capture it well.
Existing surveys focus on <1y and 10y avg leaving the medium-term somewhat neglected.
Because AIT changes the nature of medium-term inflation forecasts, existing model dynamics wont capture it well.
Existing surveys focus on <1y and 10y avg leaving the medium-term somewhat neglected.
So in order to get more realistic model estimates of expected inflation what we need are forecasts of inflation that account for medium-term overshooting (something like 2y1y inflation forecasts) and the feed these into the existing machinery
Its not easy to do econometrically but if these models are going to be leaned on we need to make sure their underlying assumptions allows them to answer informatively the questions we're asking of them
Models are tools not truth.
If you want to assess expectations for AIT (an overshooting policy) you need a model structure AND set of estimated parameters that allow for inflation to overshoot its long-run equilibrium over a 3-7y horizon so avg inflation = 2% when inflation <2%
If you want to assess expectations for AIT (an overshooting policy) you need a model structure AND set of estimated parameters that allow for inflation to overshoot its long-run equilibrium over a 3-7y horizon so avg inflation = 2% when inflation <2%
TBC: DKW, KW, and ACM are benchmarks which inspired me, even if my papers were largely response to my perceptions of their problems
But they were built in and for the Great Moderation & describe that world incredibly well but the GFC broke a lot of their structural assumptions
But they were built in and for the Great Moderation & describe that world incredibly well but the GFC broke a lot of their structural assumptions
